Title: Matrix-based homomorphic encryption-using random prime numbers

Authors: Sonam Mittal; Ketti Ramachandran Ramkumar

Addresses: Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India ' Chitkara University Institute of Engineering and Technology, Chitkara University, Punjab, India

Abstract: Cloud service providers (CSPs) provide security to data during communication and storage, but data security during computation remains a challenge. Homomorphic encryption facilitates the computation of the encrypted data to guarantee the confidentiality and security of the client's data. Most of the existing homomorphic encryption schemes work on bit-level plaintext and have various issues, such as large ciphertext size, impractical key size, noise growth, and more computational overhead. etc. The paper presents a homomorphic encryption algorithm based on integer numbers which uses the camouflage process and a matrix, filled with random prime numbers to transform the original plaintext to the next prime number and to have a more secure encryption scheme with reduced computational and memory overheads. The comparative analysis shows the memory requirement, ciphertext size, and key length as 4,896 bytes, 16.7 digits, and 3.6 digits for variant 1 and 4,855 bytes, 17.1 and 3.5 digits for variant 2 are less than existing standards.

Keywords: homomorphic encryption; security; random prime numbers; substitutional matrix; camouflage process; cloud service providers; CSPs.

DOI: 10.1504/IJESDF.2026.152235

International Journal of Electronic Security and Digital Forensics, 2026 Vol.18 No.2, pp.125 - 156

Received: 17 Feb 2024
Accepted: 30 Apr 2024
Published online: 12 Mar 2026 *

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